This work proposes a new approach to free-breathing high resolution MRI scans. Deformable motion models will be driven by the data along with a navigator signal to estimate the image and its velocity fields within an iterative reconstruction. This approach will be combined with compressed sensing methods, in order to further constrain the solution. Each of the approaches complements the other so that their combination is likely to yield greatly improved images. The approach will be used in the application of imaging late gadolinium enhancement (LGE) in the heart, and in particular imaging LGE in the left atrium. This is motivated by new studies showing that atrial fibrillation and its treatment can be characterized by the amount and location of fibrosis or LGE in the left atrium, and the challenges associated with imaging a thin-walled moving structure. Specific aims are (1) To combine iterative reconstructions employing sparsity constraints with motion models and develop and test the methods with realistic computer simulations and initial test subjects. (2) To make the reconstruction times clinically practical with implementations on GPUs and to test the new methods for obtaining high resolution 3D images of LGE in the left atrium in humans being treated for atrial fibrillation. Methods: Our multi-disciplinary team will develop advanced combined reconstruction methods that include compensation for respiratory motion for Cartesian and hybrid radial 3D LGE sequences. Simulations, test patient data, and a series of patients with atrial fibrillation will be used to develop and test the methods. A variety of tests from difference and blur metrics to image quality ranked by physicians will be employed. The development and use of accurate high resolution free-breathing LGE imaging will improve the assessment of myocardial disease and accelerate evaluation of clinical therapies.